Stabilty and Bifurcatuons of Periodic Moton in a Two-degree-of-freedom Vibro-Impact System

A two-degree-of-freedom vibro-impact system is discussed in this paper.Based on the solutions of differential equations between impacts,impact conditions and match conditions of periodic motion,the four-dimension Poincare maps of n-1 periodic motion are established.The stability of the periodic motions is investigated by the Poincare map and numerical simulation.Hopf bifurcation,subharmonic in strong resonance case and multi-impact periodic motion are analyzed by local bifurcation criterion and numerical simulation.As controlling parameter varies further,the routes of quasi-periodic impact motions to chaos are studied.It is possible to optimize practical system parameters by investigation of bifurcation and chaos.